The adiabatic approximation for coupled oscillators
β Scribed by Gregory S. Ezra
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 478 KB
- Volume
- 101
- Category
- Article
- ISSN
- 0009-2614
No coin nor oath required. For personal study only.
β¦ Synopsis
The adiabatic approlrbnation is applied to determine the quantum states of coupled oscillators described by ageneralized H&on-Heiles hamiltonian. Comparison with exact quantum and other results show that numerically calculated adiabatic energy levels are accurate even for excited states.
π SIMILAR VOLUMES
Two different adiabstic methods are applied to the czkufrttion ofener~!\* IevcIs for n t~~.o-dimensional s~stcm modefin~ 3n anIwmonic S-H stretch and an associated lsarmoriic bend coupled through centrifugai stretching The two methods are compared in their ability to yield wxurate eigenvnlues for t
Now that ab initio quantum chemistry is capable of calculating vibrational frequencies ' to an accuracy of a few cm-1 ,, it becomes interesting to examine the magnitude of small contributions. We examine the magnitude of the diagonal Born-Oppenheimer correction on the bondlengths and frequencies of
We present an elementary proof that the quantum adiabatic approximation is correct up to exponentially small errors for Hamiltonians that depend analytically on the time variable. Our proof uses optimal truncation of a straightforward asymptotic expansion. We estimate the terms of the expansion with
The components of the Floquet wave function of an oscillator in various representations are correlated. The transformation from length to velocity gauge can be viewed as a change from a diabatic to an adiabatic representation in the field variable. This is shown in three different ways.